SPECTRA: Context-Conditioned Spectral Movement Primitives for Robot Skill Generalization

2026-07-08

AI Summary

This work addresses the challenge in robotic imitation learning where existing methods struggle to generate dynamically feasible trajectories while preserving the geometric structure of demonstrated tasks, often introducing path distortions through post-processing. To overcome this, the authors propose a Spectral Motion Primitives (SMP) framework that compactly represents demonstration trajectories using truncated Fourier series. A novel phase-coupling mechanism is introduced to dynamically satisfy joint velocity and acceleration constraints without altering spectral coefficients, thereby strictly preserving end-effector paths. By integrating frame-aware GMM/GMR priors with sequential inverse kinematics mapping, the approach achieves high-fidelity geometric reconstruction, stable transfer across task coordinate systems, and significantly reduced dynamic violations and jitter. Experimental validation on the Franka Panda platform demonstrates superior path fidelity and execution feasibility.

Abstract

Robot imitation learning for manipulation should preserve demonstrated task geometry while producing dynamically admissible robot motions. Existing pipelines often learn task-dependent trajectories and impose execution limits afterward through filtering, smoothing, clipping, or time scaling, which may distort task-critical end-effector paths. We propose the Spectral Movement Primitive (SMP), a frequency-domain imitation learning framework that couples task-space skill generation with joint-space execution regulation. Demonstrations are represented by truncated finite-horizon Fourier coefficients. An empirically selected low-frequency task band captures the dominant motion geometry, while higher harmonics contribute disproportionately to derivative growth. A frame-aware context-conditioned GMM/GMR prior predicts the task-band coefficients in a canonical task frame, and the resulting Cartesian trajectory is mapped to joint space through sequential inverse kinematics. A phase-coupled regulator then limits the requested phase progression without modifying the spectral coefficients, thereby enforcing joint velocity and acceleration limits while preserving the represented path. Experiments evaluate task-band reconstruction, robustness to composite demonstration corruption, out-of-distribution cross-board generalization, joint-space dynamic admissibility, end-effector path preservation, and deployment on a Franka Panda robot. Results show compact geometric reconstruction, consistent transfer across unseen task frames, substantial reductions in dynamic violations and jerk, and preservation of the intended end-effector path during phase regulation.

Problem

• robot imitation learning
• task geometry preservation
• dynamically admissible motion
• end-effector path distortion
• manipulation skills

Innovation

• Spectral Movement Primitives
• frequency-domain imitation learning
• task geometry preservation
• phase-coupled regulation
• context-conditioned GMM/GMR